1. Field of the Invention
This invention relates to bandgap voltage reference circuits, and more particularly to such circuits in which an attempt is made to correct for a T-Tln(T) deviation from a constant output voltage.
2. Description of the Related Art
Bandgap reference circuits have been developed to provide a stable voltage supply that is insensitive to temperature variations over a wide temperature range. These circuits operate on the principle of compensating the negative temperature drift of a bipolar transistor's base-emitter voltage (V.sub.be) with the positive temperature coefficient of the thermal voltage V.sub.T, which is equal to kT/q, where k is Boltzmann's constant, T is the absolute temperature in degrees Kelvin and q is the electronic charge. A known negative temperature drift associated with the V.sub.be is first generated. A positive temperature drift due to the thermal voltage is then produced, and is scaled and subtracted from the negative temperature drift to obtain a nominally zero temperature dependence. Numerous variations in the bandgap reference circuitry have been designed, and are discussed for example in Grebene, Bipolar and MOS Analog Integrated Circuit Design, John Wiley & Sons, 1984, pages 206-209, and in Fink, et al. Ed., Electronics Engineers' Handbook, 3d ed., McGraw-Hill Book Co., 1989, pages 8.48-8.50.
Although the output of a bandgap voltage cell is ideally independent of temperature, the outputs of prior cells have been found to include a term that varies with T -Tln (T), where in is the natural logarithm function. Such an output deviation is shown in FIG. 1, in which the bandgap voltage output (V.sub.bg) increases from a value of about 1.2408 volts at -50.degree. C. to about 1.244 volts at about 45.degree. C., and then returns back to about 1.2408 volts at 150.degree. C. This output deviation is not symmetrical; its peak is skewed about 5.degree. C. below the midpoint of the temperature range.
It is difficult to precisely compensate for the temperature deviation electronically, so simpler approximations have been used. One such circuit is shown in FIG. 2, and is described in U.S. Pat. No. 4,808,908 to Lewis et al., assigned to Analog Devices, Inc., the assignee of the present invention. The circuit includes bipolar npn transistors Q1 and Q2, with the emitter area of Q1 scaled larger than that of Q2 by a factor A. The emitters of Q1 and Q2 are connected together through a resistor Ra that has a relatively low temperature coefficient of resistance (TCR). A second relatively low TCR resistor Rb is connected in series with a relatively high TCR resistor Rc between the Ra/Q2 emitter junction and a negative (or ground) return voltage bus V-. Q1 and Q2 are provided with collector currents having a constant ratio, such as by connecting their collectors respectively to the inverting and non-inverting inputs of an operational amplifier. Ra and Rb are preferably implemented as thin film resistors, with TCRs on the order of 30 ppm (parts per million)/.degree. C. Rc is preferably a diffused resistor having a TCR of typically 1,500-2,000 ppm/.degree. C.
The base output voltage V.sub.bg is equal to the sum of V.sub.be for Q2 and the voltage drops across Rb and Rc. In the absence of Rc, the voltage across Rb can be determined by considering the voltage across Ra. This is equal to the difference in V.sub.be for Q1 and Q2; since the emitter of Q1 is larger than the emitter of Q2 but both transistors may carry equal currents, the emitter current density of Q1 will be less than for Q2, and Q1 will accordingly exhibit a smaller V.sub.be. The V.sub.be differential between Q1 and Q2 will have the form V.sub.T ln(Id2/Id1)=V.sub.T ln(A), where I1 and I2 are the absolute emitter currents, and Id1 and Id2 are the emitter current densities of Q1 and Q2, respectively. Since I1 is preferably equal to I2, the current through Rb will be twice the current through Ra, so that the voltage across Rb will have the form (2Ra/Rb)V.sub.T ln(A). Still ignoring Rc, the described circuit will exhibit the output temperature deviation mentioned above.
The addition of high TCR resistor Rc approximates an output voltage compensation by producing a square law (T.sup.2) term that is added to V.sub.bg. Since the tail current through Rb is proportional to temperature anyway, adding a significant temperature coefficient by means of the high TCR tail resistor Rc yields a voltage across this resistance that is proportional to T.sup.2. Combining this square law voltage with the voltage across Rb and V.sub.be for Q2 approximately cancels the effect of the temperature deviation.
Rc is preferably a diffused resistor, which is not subject to trimming. However, the resistance values of thin film resistors Ra and Rb can be conveniently adjusted by laser trimming to minimize the first and second derivatives of the bandgap cell output as a function of temperature.
Unfortunately, the square law voltage compensation produced by the FIG. 2 circuit is symmetrical, as opposed to the skewed parabolic shape of the temperature deviation that actually characterizes the bandgap cell. Thus, the voltage correction that can be achieved with the FIG. 2 circuit is limited, and a significant residual temperature coefficient is left in both the upper and lower portions of the temperature range.